Problem: Express your answer as a mixed number simplified to lowest terms. $9\dfrac{2}{18}-3\dfrac{2}{3} = {?}$
Simplify each fraction. $= {9\dfrac{1}{9}} - {3\dfrac{2}{3}}$ Find a common denominator for the fractions: $= {9\dfrac{1}{9}}-{3\dfrac{6}{9}}$ Convert ${9\dfrac{1}{9}}$ to ${8 + \dfrac{9}{9} + \dfrac{1}{9}}$ So the problem becomes: ${8\dfrac{10}{9}}-{3\dfrac{6}{9}}$ Separate the whole numbers from the fractional parts: $= {8} + {\dfrac{10}{9}} - {3} - {\dfrac{6}{9}}$ Bring the whole numbers together and the fractions together: $= {8} - {3} + {\dfrac{10}{9}} - {\dfrac{6}{9}}$ Subtract the whole numbers: $=5 + {\dfrac{10}{9}} - {\dfrac{6}{9}}$ Subtract the fractions: $= 5+\dfrac{4}{9}$ Combine the whole and fractional parts into a mixed number: $= 5\dfrac{4}{9}$